Overdispersion in environmental count data

Question

Why do Poisson models often fail with environmental count data?

Short answer

Poisson models assume that the mean and variance are approximately equal. In real environmental datasets, the variance is often much larger than the mean. This is called overdispersion.

Simple example

counts <- c(0, 1, 2, 3, 5, 8, 13, 21, 34)

mean(counts)

[1] 9.666667

var(counts)

[1] 128.5

Interpretation

If the variance is much larger than the mean, a basic Poisson model may underestimate uncertainty. In that case, a negative binomial model is often more appropriate.

Why this matters

Environmental count data often include clustering, missing drivers, spatial heterogeneity, reporting bias, and temporal variation. These patterns can make simple count models too optimistic.